Memory retention decays in time monotonically, if the memorized information is not reviewed or recalled and used in subsequent mental activities. The well-known spacing effect posits that temporally spaced presentations and reviews yield substantially better learning results and efficiency than massed presentations and iterations do.
With the development of computer technology, now various computer-aided learning system and method with adaptive optimization have appeared, if better understood and employed the spacing effect, it could significantly benefit learning processes in classroom or computer-aided instructions. The existing computer-aided learning systems and methods with adaptive optimization are mostly utilized the characteristic of mass storage capacity and high interaction, attracting learners by multimedia, and the spacing effect is far from widespread and systematic. Even in the touted spacing-effect applications, the adopted strategy of spaced presentations or reviews is mostly qualitative in nature and based on certain empirical data from experiments that are of questionable relevance to the concerned learning practices. Often enough, such strategies are not personalized, but rather of the “one size fits all” kind, that neglect any difference between individual learners.
When a grey-box model (also known as semi-physical model) is available based on insights into the system, induction of experimental observations, or general considerations of symmetry and conservation laws, the concerned dynamics is represented by predetermined mathematical formulas or transformations, with unknown parameters to be determined by stochastic filtering. Such mode is known as parametric system identification. By contrast, nonparametric system identification works with a black-box model when no mathematical formula or transformation is known or considered suitable for the system of interest. Nevertheless, mathematics is still indispensable to proceed quantitatively. For such nonparametric system identification applications, the mostly employed mathematical models and utilities include the Volterra or Wiener expansions. Unfortunately, for the dynamics of learning and forgetting, no semi-physical model has been conceived that is generally applicable and widely accepted, whereas nonparametric models may have to involve a large number of unknown degrees of freedom, that are difficult to determine within reasonable accuracy from a limited amount of observation data. Even though it proves hard to frame the dynamics of learning and forgetting into a mathematical model, either grey-box or black-box, there may be little doubt that the process of learning and forgetting is governed by deterministic principles or rules, albeit not visible to us, judging from the excellent reproducibility of many effects and phenomena concerning human memory.